I don't, in fact, speak Japanese as a functional language, or pretend to any deep cultural knowledge of Japan. So sort of your second option; I'd be emitting that noise expecting to trigger the same concept that would be triggered by the common translation "do your best" in an English speaker (with the extra warm glow of anime-fan group affiliation).
And I probably wouldn't do so to an actual native speaker, because of paranoia that I'm not properly modeling their experience, which may not make sense.
Is there any rationalist equivalent of "good luck"? I've tried a few variants, such as "work well", "knock them dead", "we're with you" and certain situation-specific phrasings, but haven't found anything that worked generally - though a hearty "may all the gods of Olympus be with you!" can serve. Not a vitally important point, but it would be nice to have something similarly supportive and yet accurate to say.